数学科学研究所
Insitute of Mathematical Science

A characterization of Projectively Flat manifolds

Seminar | Institute of Mathematical Sciences

Time:10:30-11:30, Dec 20, Thursday

LocationRoom 302, Library


Speaker: Simone Calamai,  Universita delgi Studi di Firenze


Title: A characterization of Projectively Flat manifolds


Abstract: We define a partition of the space of projectively flat metrics in three classes according to the sign
of the Chern scalar curvature; we show that the class of negative projectively flat metrics is empty, and the class of positive projectively flat metrics consists precisely of locally conformally flat-Kaehler metrics on Hopf manifolds, explicitly characterized by Vaisman. If time allows, we review the known characterization and properties of zero projectively flat metrics. As applications, we make sharp the list of possible projectively flat metrics by Li, Yau, and Zheng.


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